# Graph y=-5sin(4/3x)

Graph y=-5sin(4/3x)
Use the form to find the variables used to find the amplitude, period, phase shift, and vertical shift.
Find the amplitude .
Amplitude:
Find the period of .
The period of the function can be calculated using .
Replace with in the formula for period.
is approximately which is positive so remove the absolute value
Multiply the numerator by the reciprocal of the denominator.
Cancel the common factor of .
Factor out of .
Factor out of .
Cancel the common factor.
Rewrite the expression.
Combine and .
Move to the left of .
Find the phase shift using the formula .
The phase shift of the function can be calculated from .
Phase Shift:
Replace the values of and in the equation for phase shift.
Phase Shift:
Multiply the numerator by the reciprocal of the denominator.
Phase Shift:
Multiply by .
Phase Shift:
Phase Shift:
Find the vertical shift .
Vertical Shift:
List the properties of the trigonometric function.
Amplitude:
Period:
Phase Shift: ( to the right)
Vertical Shift:
Select a few points to graph.
Find the point at .
Replace the variable with in the expression.
Simplify the result.
Cancel the common factor of and .
Factor out of .
Cancel the common factors.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Divide by .
Multiply by .
The exact value of is .
Multiply by .
Find the point at .
Replace the variable with in the expression.
Simplify the result.
Combine and .
Multiply by .
Reduce the expression by cancelling the common factors.
Factor out of .
Factor out of .
Cancel the common factor.
Rewrite the expression.
Multiply the numerator by the reciprocal of the denominator.
Cancel the common factor of .
Factor out of .
Cancel the common factor.
Rewrite the expression.
The exact value of is .
Multiply by .
Find the point at .
Replace the variable with in the expression.
Simplify the result.
Combine and .
Multiply by .
Reduce the expression by cancelling the common factors.
Reduce the expression by cancelling the common factors.
Factor out of .
Factor out of .
Cancel the common factor.
Rewrite the expression.
Divide by .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.
The exact value of is .
Multiply by .
Find the point at .
Replace the variable with in the expression.
Simplify the result.
Combine and .
Multiply by .
Reduce the expression by cancelling the common factors.
Factor out of .
Factor out of .
Cancel the common factor.
Rewrite the expression.
Multiply the numerator by the reciprocal of the denominator.
Cancel the common factor of .
Factor out of .
Cancel the common factor.
Rewrite the expression.
Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because sine is negative in the fourth quadrant.
The exact value of is .
Multiply by .
Multiply by .
Find the point at .
Replace the variable with in the expression.
Simplify the result.
Combine and .
Multiply by .
Reduce the expression by cancelling the common factors.
Reduce the expression by cancelling the common factors.
Factor out of .
Factor out of .
Cancel the common factor.
Rewrite the expression.
Divide by .
Cancel the common factor of and .
Factor out of .
Cancel the common factors.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Divide by .
Subtract full rotations of until the angle is greater than or equal to and less than .
The exact value of is .
Multiply by .
List the points in a table.
The trig function can be graphed using the amplitude, period, phase shift, vertical shift, and the points.
Amplitude:
Period:
Phase Shift: ( to the right)
Vertical Shift:
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### Name

Name eighty-six million four hundred thirty-three thousand fifty-two

### Interesting facts

• 86433052 has 32 divisors, whose sum is 205326000
• The reverse of 86433052 is 25033468
• Previous prime number is 373

### Basic properties

• Is Prime? no
• Number parity even
• Number length 8
• Sum of Digits 31
• Digital Root 4

### Name

Name five hundred eighty-five million three hundred fifty-one thousand twenty-nine

### Interesting facts

• 585351029 has 4 divisors, whose sum is 585527040
• The reverse of 585351029 is 920153585
• Previous prime number is 3391

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 9
• Sum of Digits 38
• Digital Root 2

### Name

Name three hundred six million five hundred forty-three thousand four hundred thirty-five

### Interesting facts

• 306543435 has 64 divisors, whose sum is 566853120
• The reverse of 306543435 is 534345603
• Previous prime number is 277

### Basic properties

• Is Prime? no
• Number parity odd
• Number length 9
• Sum of Digits 33
• Digital Root 6